Entanglement-Enabled Advantage for Learning a Bosonic Random Displacement Channel.

We show that quantum entanglement can provide an exponential advantage in learning properties of a bosonic continuous-variable (CV) system. The task we consider is estimating a probabilistic mixture of displacement operators acting on n bosonic modes, called a random displacement channel. We prove that if the n modes are not entangled with an ancillary quantum memory, then the channel must be sampled a number of times exponential in n in order to estimate its characteristic function to reasonable precision; this lower bound on sample complexity applies even if the channel inputs and measurements performed on channel outputs are chosen adaptively or have unrestricted energy.

Universal Spreading of Conditional Mutual Information in Noisy Random Circuits.

We study the evolution of conditional mutual information (CMI) in generic open quantum systems, focusing on one-dimensional random circuits with interspersed local noise. Unlike in noiseless circuits, where CMI spreads linearly while being bounded by the light cone, we find that noisy random circuits with an error rate p exhibit superlinear propagation of CMI, which diverges far beyond the light cone at a critical circuit depth t_{c}∝p^{-1}. We demonstrate that the underlying mechanism for such rapid spreading is the combined effect of local noise and a scrambling unitary, which selectively removes short-range correlations while preserving long-range correlations.

Tight Bounds on Pauli Channel Learning without Entanglement.

Quantum entanglement is a crucial resource for learning properties from nature, but a precise characterization of its advantage can be challenging. In this Letter, we consider learning algorithms without entanglement to be those that only utilize states, measurements, and operations that are separable between the main system of interest and an ancillary system. Interestingly, we show that these algorithms are equivalent to those that apply quantum circuits on the main system interleaved with mid-circuit measurements and classical feedforward.

Spoofing Cross-Entropy Measure in Boson Sampling.

Cross-entropy (XE) measure is a widely used benchmark to demonstrate quantum computational advantage from sampling problems, such as random circuit sampling using superconducting qubits and boson sampling (BS). We present a heuristic classical algorithm that attains a better XE than the current BS experiments in a verifiable regime and is likely to attain a better XE score than the near-future BS experiments in a reasonable running time. The key idea behind the algorithm is that there exist distributions that correlate with the ideal BS probability distribution and that can be efficiently computed.

Classical Simulation of Boson Sampling Based on Graph Structure.

Boson sampling is a fundamentally and practically important task that can be used to demonstrate quantum supremacy using noisy intermediate-scale quantum devices. In this Letter, we present classical sampling algorithms for single-photon and Gaussian input states that take advantage of a graph structure of a linear-optical circuit. The algorithms' complexity grows as so-called treewidth, which is closely related to the connectivity of a given linear-optical circuit.

Quantum Metrological Power of Continuous-Variable Quantum Networks.

We investigate the quantum metrological power of typical continuous-variable (CV) quantum networks. Particularly, we show that most CV quantum networks provide an entanglement to quantum states in distant nodes that enables one to achieve the Heisenberg scaling in the number of modes for distributed quantum displacement sensing, which cannot be attained using an unentangled probe state. Notably, our scheme only requires local operations and measurements after generating an entangled probe using the quantum network.

Quantum Limits of Superresolution in a Noisy Environment.

We analyze the ultimate quantum limit of resolving two identical sources in a noisy environment. We prove that in the presence of noise causing false excitation, such as thermal noise, the quantum Fisher information of arbitrary quantum states for the separation of the objects, which quantifies the resolution, always converges to zero as the separation goes to zero. Noisy cases contrast with noiseless cases where the quantum Fisher information has been shown to be nonzero for a small distance in various circumstances, revealing the superresolution.

Probing Bayesian Credible Regions Intrinsically: A Feasible Error Certification for Physical Systems.

Standard computation of size and credibility of a Bayesian credible region for certifying any point estimator of an unknown parameter (such as a quantum state, channel, phase, etc.) requires selecting points that are in the region from a finite parameter-space sample, which is infeasible for a large dataset or dimension as the region would then be extremely small. We solve this problem by introducing the in-region sampling theory to compute both region qualities just by sampling appropriate functions over the region itself using any Monte Carlo sampling method.

Minimal control power of controlled dense coding and genuine tripartite entanglement.

We investigate minimal control power (MCP) for controlled dense coding defined by the channel capacity. We obtain MCPs for extended three-qubit Greenberger-Horne-Zeilinger (GHZ) states and generalized three-qubit W states. Among those GHZ states, the standard GHZ state is found to maximize the MCP and so does the standard W state among the W-type states.